how do I solve 60*3^(x/8) = 30*2(x/5)

Answer 1

I made a typo the equation is: 60*3^(x/8) = 30*2^(x/5)

Answer 2

60*3^(x/8) = 30*2^(x/5)
2 * 3^(x/8) = 2^(x/5)
log2 + x/8 log3 = x/5 log2
x (log2/5 - log3/8) = log2
x = log2/(log2/5 - log3/8) = 532

Answer 3

I would divide both sides by 30
2*3^(x/8) = 2^(x/5)
log both sides, and use basic log rules
log 2 + (x/8)log3 = (x/5)log2
x[ (1/5)log2 - (1/8)log3 ] = log2

now go to your calculator and evaluate, I got x = appr. 532.00

Your calculator will kick into scientific notation since the numbers are really big. If you have a half-decent calculator it should have more than one memory storages, use them to store in-between answers to get my answer.

Don't know what the purpose of solving such an equation serves,
the equation does not really represent anything measurably in
a real world.

Answer 4

actually, the original problem was

Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60 bacteria and the number of bacteria was tripling every 8 days. Bacteria B had a population of 30 bacteria and was doubling every 5 days. Determine the number of days it will take for both bacteria cultures to have the same population.

Answer 5

Sry guys for not responding I forgot I posted here.
I have already solved it.